How to deal with very, very small time-series?
Of course depends on your type of data, but Holt-Winter models can have different degree of complexity and use moving average, trend, and seasonality. This is most useful if the data is not hierarchical, meaning that the time-series are independent from each other.
If time-series are relatives of each other then you can also try aggregating them, predict at aggregate level and then disaggregate. The following can be a good resource:
https://otexts.com/fpp2/